In: Donatelli, Susanna; Kleijn, Jetty: Lecture Notes in Computer Science, Vol. 1630: Application and Theory of Petri Nets 1999, 20th International Conference, ICATPN'99, Williamsburg, Virginia, USA, pages 324-343. Springer-Verlag, June 1999.
Abstract: In this paper we study properties of an abstract and (as we hope) a uniform frame for Petri net models, which enables us to generalise algebra as well as enabling rule of Petri nets. Our approach of such a frame is based on using partial groupoids in Petri nets. Properties of Petri nets constructed in this manner are investigated through related labelled transition systems. In particular, we investigate the relationships between properties of partial groupoids used in Petri nets and properties of transition systems crucial for the existence of the state equation and linear algebraic techniques. We show that partial groupoids embeddable into Abelian groups play an important role in preserving these properties.